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In the given figure, AP, AQ and BC are tangents to the circle. If AB = 5 cm, AC = 6 cm and BC = 4 cm then the length of AP is
Let tangent BC touch the circle at point R
As we know tangents drawn from an external point to a circle are equal.
We have
AP = AQ
[tangents from point A]
BP = BR …[1]
[tangents from point B]
CQ = CR …[2]
[tangents from point C]
Now,
AP = AQ
⇒ AB + BP = AC + CQ
⇒ 5 + BR = 6 + CR [From 1 and 2]
⇒CR = BR - 1 …[3]
Now,
BC = 4 cm
BR + CR = 4
BR + BR - 1 = 4 [Using 3]
2BR = 5 cm
BR = 2.5 cm
BP = BR = 2.5 cm [Using 2]
AP = AB + BP = 5 + 2.5 = 7.5 cm